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As quoted in Eruvin 14a, from Kings I 7:23, we know that Shlomo's pool was round, measuring 10 across and 30 around. There have been discussions about how the ratio of these (3:1) is only an approximation to pi, or that it deals only with significant figures.

Are there any sources that deal with the possibility that the pool was not circular, but rather an ellipse? A major axis of 5 and minor axis of 4.543 would give a circumference of 30. Are these any other places where sources discuss elliptical shapes as ways of resolving a seeming contradiction?

Of course, this is separate from the discussion in the daf regarding the shape of the 3D pool. The calculation of volume would have to change to accommodate the difference in area of the top (ellipse would have an area even smaller than the circle).

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    – Dov
    Sep 21 '20 at 16:42
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    I'm not holding in the Hebrew math terms but maybe check out daf-yomi.com/Data/UploadedFiles/DY_Item/21447-sFile.pdf page 5.
    – robev
    Sep 21 '20 at 20:13
  • Some Meforshim explain that the reason for the pasuk telling us the ratio of the pool is to provide a halachic approximation for pi. Otherwise we'd just figure it out ourselves. If it was elliptical, though, what would be the point?
    – Rafael
    Sep 22 '20 at 1:12
  • Is assuming an imprecisely specified ellipse any better than assuming an imprecise circumference?
    – Double AA ♦
    Sep 22 '20 at 1:50
  • An ellipse would lead to other calculations regarding the shape of the walls from top to bottom than the end of the discussion in the Gemara (of 3 straight and 2 curved). The long article linked below, plus the reference from it that I've identified indicate how the volume calculations would shift.
    – Yakov Pechersky
    Sep 22 '20 at 15:43
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While that may help in one instance, it is a general principle that numbers used in the math of the Bible and Talmud are rounded. For example, the Talmud always treats the diagonal of a square as being seven fifths of the length of a side, even though the mathematical ratio is the square root of two, or 1.41.

Here are a couple links to people who dealt with your question, one short and another long and detailed.

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    I don't see how this answers the question at all (nor how the linked-to source sheet and article do). The question at hand seeks sources for saying the pool was an ellipse. This answer neither provides nor points to any such sources, nor provides any evidence that they don't exist. -1.
    – msh210 ♦
    Sep 22 '20 at 5:07
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    Actually, the second link does provide a reference to "Solomon's sea and pi" by Simoson, which does discuss ellipses and related shapes. A PDF of it can be found at searching for it online.
    – Yakov Pechersky
    Sep 22 '20 at 15:41

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